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Mirrors > Home > ILE Home > Th. List > cbvreu | Unicode version |
Description: Change the bound variable of a restricted unique existential quantifier using implicit substitution. (Contributed by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
cbvral.1 | |
cbvral.2 | |
cbvral.3 |
Ref | Expression |
---|---|
cbvreu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1493 | . . . 4 | |
2 | 1 | sb8eu 1990 | . . 3 |
3 | sban 1906 | . . . 4 | |
4 | 3 | eubii 1986 | . . 3 |
5 | clelsb3 2222 | . . . . . 6 | |
6 | 5 | anbi1i 453 | . . . . 5 |
7 | 6 | eubii 1986 | . . . 4 |
8 | nfv 1493 | . . . . . 6 | |
9 | cbvral.1 | . . . . . . 7 | |
10 | 9 | nfsb 1899 | . . . . . 6 |
11 | 8, 10 | nfan 1529 | . . . . 5 |
12 | nfv 1493 | . . . . 5 | |
13 | eleq1 2180 | . . . . . 6 | |
14 | sbequ 1796 | . . . . . . 7 | |
15 | cbvral.2 | . . . . . . . 8 | |
16 | cbvral.3 | . . . . . . . 8 | |
17 | 15, 16 | sbie 1749 | . . . . . . 7 |
18 | 14, 17 | syl6bb 195 | . . . . . 6 |
19 | 13, 18 | anbi12d 464 | . . . . 5 |
20 | 11, 12, 19 | cbveu 2001 | . . . 4 |
21 | 7, 20 | bitri 183 | . . 3 |
22 | 2, 4, 21 | 3bitri 205 | . 2 |
23 | df-reu 2400 | . 2 | |
24 | df-reu 2400 | . 2 | |
25 | 22, 23, 24 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wnf 1421 wcel 1465 wsb 1720 weu 1977 wreu 2395 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-cleq 2110 df-clel 2113 df-reu 2400 |
This theorem is referenced by: cbvrmo 2630 cbvreuv 2633 |
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